Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
831 conjugacy classes of subgroups.
The subgroup lattice has 674 nodes — too large to display as a diagram.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #10596293 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#5822 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | #10594795 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#5234 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | #10591073 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 6 | #10591070 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | #10589159 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 8 | #72121 | — | 3 | 1 | no | maximal |
| 9 | #70013 | — | 3 | 1 | no | maximal |
| 10 | C2×C32×#41 | C22 | 1 | 1 | yes | characteristic |
| 11 | C2×#3828 | C22 | 1 | 1 | yes | characteristic |
| 12 | C2×C3×#235 | C22 | 1 | 1 | yes | characteristic |
| 13 | #64160 | — | 2 | 1 | no | — |
| 14 | #64159 | — | 2 | 2 | no | — |
| 15 | #64158 | — | 2 | 1 | no | — |
| 16 | #64151 | — | 2 | 1 | no | — |
| 17 | #64141 | — | 2 | 1 | no | — |
| 18 | C2×#3748 | C22 | 1 | 1 | yes | characteristic |
| 19 | C3×#951 | — | 2 | 1 | no | — |
| 20 | C3×#950 | — | 2 | 2 | no | — |
| 21 | C3×#949 | — | 2 | 1 | no | — |
| 22 | C3×#942 | — | 2 | 1 | no | — |
| 23 | C3×#932 | — | 2 | 1 | no | — |
| 24 | C2×C3×#208 | C22 | 1 | 1 | yes | characteristic |
| 25 | C2×C3×#208 | C22 | 1 | 1 | yes | characteristic |
| 26 | C22×C3×C3⋊C8 | C22 | 1 | 1 | yes | characteristic |
| 27 | #63833 | — | 2 | 1 | no | — |
| 28 | #63831 | — | 2 | 1 | no | — |
| 29 | #63830 | — | 2 | 1 | no | — |
| 30 | #63829 | — | 2 | 2 | no | — |
| 31 | #63825 | — | 2 | 1 | no | — |
| 32 | C3×#830 | — | 2 | 2 | no | — |
| 33 | #63557 | — | 2 | 2 | no | — |
| 34 | (C2×D3)⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 35 | C3×#575 | — | 3 | 1 | no | — |
| 36 | #5822 | — | 3 | 1 | no | — |
| 37 | #5822 | — | 3 | 1 | no | — |
| 38 | #5822 | — | 3 | 1 | no | — |
| 39 | #5822 | — | 6 | 1 | no | — |
| 40 | #5822 | D3 | 1 | 1 | yes | characteristic, complemented |
| 41 | #5748 | — | 3 | 1 | no | — |
| 42 | C3×#408 | — | 3 | 1 | no | — |
| 43 | #5234 | — | 3 | 1 | no | — |
| 44 | #5234 | D3 | 1 | 1 | yes | characteristic, complemented |
| 45 | #5129 | — | 3 | 1 | no | — |
| 46 | #5110 | — | 3 | 1 | no | — |
| 47 | #5110 | — | 3 | 1 | no | — |
| 48 | C3⋊#338 | — | 3 | 1 | no | — |
| 49 | C3⋊#338 | — | 3 | 1 | no | — |
| 50 | C32×#41 | — | 2 | 1 | no | — |
| 51 | C32×#41 | — | 2 | 1 | no | — |
| 52 | C32×#41 | — | 2 | 1 | no | — |
| 53 | C32×#41 | — | 2 | 1 | no | — |
| 54 | C2×C32×Q8 | D4 | 1 | 1 | yes | characteristic |
| 55 | C2×C32×D4 | — | 2 | 1 | no | — |
| 56 | C2×C32×D4 | D4 | 1 | 1 | yes | characteristic |
| 57 | C22×C32×C4 | — | 2 | 1 | no | — |
| 58 | C22×C32×C4 | C23 | 1 | 1 | yes | characteristic |
| 59 | C2×#638 | — | 2 | 1 | no | — |
| 60 | #3828 | — | 2 | 1 | no | — |
| 61 | #3828 | — | 2 | 1 | no | — |
| 62 | #3828 | — | 2 | 1 | no | — |
| 63 | #3828 | — | 2 | 1 | no | — |
| 64 | C2×C4⋊(C3⋊D3) | D4 | 1 | 1 | yes | characteristic |
| 65 | C2×C4×C3⋊D3 | — | 2 | 1 | no | — |
| 66 | C2×#634 | D4 | 1 | 1 | yes | characteristic |
| 67 | C2×C3×#67 | — | 2 | 1 | no | — |
| 68 | C3×#235 | — | 2 | 1 | no | — |
| 69 | C3×#235 | — | 2 | 1 | no | — |
| 70 | C3×#235 | — | 2 | 1 | no | — |
| 71 | C3×#235 | — | 2 | 1 | no | — |
| 72 | C2×C3×D12 | D4 | 1 | 1 | yes | characteristic |
| 73 | C2×C3×C4×D3 | — | 2 | 1 | no | — |
| 74 | C2×C3×Dic6 | D4 | 1 | 1 | yes | characteristic |
| 75 | #3756 | — | 2 | 2 | no | — |
| 76 | #3755 | — | 2 | 2 | no | — |
| 77 | #3754 | — | 2 | 2 | no | — |
| 78 | #3753 | — | 2 | 2 | no | — |
| 79 | #3748 | — | 2 | 1 | no | — |
| 80 | #3748 | — | 2 | 1 | no | — |
| 81 | C2×C3⋊(C3⋊C8) | D4 | 1 | 2 | yes | — |
| 82 | C3×#216 | — | 2 | 2 | no | — |
| 83 | C3×#215 | — | 2 | 2 | no | — |
| 84 | C3×#214 | — | 2 | 2 | no | — |
| 85 | C3×#213 | — | 2 | 2 | no | — |
| 86 | C3×#208 | — | 2 | 1 | no | — |
| 87 | C3×#208 | — | 2 | 1 | no | — |
| 88 | C3×#208 | — | 2 | 1 | no | — |
| 89 | C3×#208 | — | 2 | 1 | no | — |
| 90 | C2×C3×C3⋊C8 | — | 2 | 1 | no | — |
| 91 | C2×C3×C3⋊C8 | — | 2 | 1 | no | — |
| 92 | C2×C3×C3⋊C8 | — | 2 | 1 | no | — |
| 93 | C2×C3×C3⋊C8 | D4 | 1 | 2 | yes | — |
| 94 | C2×C3×C3⋊C8 | D4 | 1 | 2 | yes | — |
| 95 | #3719 | — | 2 | 2 | no | — |
| 96 | #3717 | — | 2 | 2 | no | — |
| 97 | #3716 | — | 2 | 2 | no | — |
| 98 | #3714 | — | 2 | 2 | no | — |
| 99 | #2017 | — | 9 | 1 | no | Sylow |
| 100 | C2×C3×#41 | — | 2 | 1 | no | — |
| 101 | C2×C3×#41 | — | 3 | 1 | no | — |
| 102 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 103 | C2×C3×#41 | C2×D3 | 1 | 1 | yes | characteristic |
| 104 | C2×#235 | — | 3 | 1 | no | — |
| 105 | C2×#235 | — | 3 | 1 | no | — |
| 106 | C2×#235 | — | 6 | 1 | no | — |
| 107 | C2×#235 | C2×D3 | 1 | 1 | yes | characteristic |
| 108 | C3×#137 | — | 6 | 1 | no | — |
| 109 | C3×#137 | — | 6 | 1 | no | — |
| 110 | C3×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 111 | C3×AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 112 | C3×#135 | — | 6 | 2 | no | — |
| 113 | C2×C3×M16 | — | 3 | 1 | no | — |
| 114 | C2×C3×M16 | — | 3 | 1 | no | — |
| 115 | C22×C3×C8 | — | 3 | 1 | no | — |
| 116 | #951 | — | 2 | 1 | no | — |
| 117 | #951 | — | 6 | 1 | no | — |
| 118 | #951 | — | 6 | 1 | no | — |
| 119 | #951 | — | 6 | 1 | no | — |
| 120 | #951 | — | 6 | 2 | no | — |
| 121 | #950 | — | 2 | 2 | no | — |
| 122 | #950 | — | 6 | 2 | no | — |
| 123 | #950 | — | 6 | 2 | no | — |
| 124 | #950 | — | 6 | 4 | no | — |
| 125 | #950 | — | 6 | 2 | no | — |
| 126 | #949 | — | 2 | 1 | no | — |
| 127 | #949 | — | 6 | 1 | no | — |
| 128 | #949 | — | 6 | 1 | no | — |
| 129 | #949 | — | 6 | 1 | no | — |
| 130 | #949 | — | 6 | 2 | no | — |
| 131 | #942 | — | 2 | 1 | no | — |
| 132 | #942 | — | 6 | 1 | no | — |
| 133 | #942 | — | 6 | 2 | no | — |
| 134 | #942 | — | 6 | 1 | no | — |
| 135 | #942 | — | 6 | 1 | no | — |
| 136 | #932 | — | 2 | 1 | no | — |
| 137 | #932 | — | 6 | 1 | no | — |
| 138 | #932 | — | 6 | 2 | no | — |
| 139 | #932 | — | 6 | 1 | no | — |
| 140 | #932 | — | 6 | 1 | no | — |
| 141 | C2×#208 | — | 3 | 1 | no | — |
| 142 | C2×#208 | — | 3 | 1 | no | — |
| 143 | C2×#208 | — | 6 | 1 | no | — |
| 144 | C2×#208 | C2×D3 | 1 | 1 | yes | characteristic |
| 145 | C2×#208 | C2×D3 | 1 | 1 | yes | characteristic |
| 146 | C22×C3⋊C8 | C2×D3 | 1 | 1 | yes | characteristic |
| 147 | #909 | — | 6 | 1 | no | — |
| 148 | #909 | — | 6 | 1 | no | — |
| 149 | #908 | — | 6 | 1 | no | — |
| 150 | #908 | — | 6 | 1 | no | — |
| 151 | #904 | — | 6 | 2 | no | — |
| 152 | C3×C22⋊C8 | — | 6 | 2 | no | — |
| 153 | #830 | — | 2 | 2 | no | — |
| 154 | #830 | — | 6 | 2 | no | — |
| 155 | (C2×D3)⋊C8 | — | 6 | 2 | no | — |
| 156 | (C2×D3)⋊C8 | — | 6 | 2 | no | — |
| 157 | (C2×D3)⋊C8 | — | 6 | 2 | no | — |
| 158 | C23×C32 | — | 2 | 1 | no | — |
| 159 | C23×C32 | #41 | 1 | 1 | yes | characteristic |
| 160 | C22×C3⋊D3 | — | 2 | 1 | no | — |
| 161 | C22×C3×D3 | — | 2 | 1 | no | — |
| 162 | C32×Q8 | — | 2 | 1 | no | — |
| 163 | C32×Q8 | — | 2 | 1 | no | — |
| 164 | C32×D4 | — | 2 | 1 | no | — |
| 165 | C32×D4 | — | 2 | 1 | no | — |
| 166 | C32×D4 | — | 4 | 1 | no | — |
| 167 | C32×D4 | — | 4 | 1 | no | — |
| 168 | C2×C32×C4 | — | 2 | 1 | no | — |
| 169 | C2×C32×C4 | — | 4 | 1 | no | — |
| 170 | C2×C32×C4 | — | 4 | 1 | no | — |
| 171 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 172 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 173 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 174 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 175 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 176 | C2×C32×C4 | C2×D4 | 1 | 1 | yes | characteristic |
| 177 | #638 | — | 4 | 1 | no | — |
| 178 | #638 | — | 4 | 1 | no | — |
| 179 | C2×C3⋊Dic3 | — | 2 | 1 | no | — |
| 180 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 181 | C4⋊(C3⋊D3) | — | 2 | 1 | no | — |
| 182 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 183 | C4×C3⋊D3 | — | 4 | 1 | no | — |
| 184 | #634 | — | 2 | 1 | no | — |
| 185 | #634 | — | 2 | 1 | no | — |
| 186 | C3×#67 | — | 4 | 1 | no | — |
| 187 | C3×#67 | — | 4 | 1 | no | — |
| 188 | C2×C3×Dic3 | — | 2 | 1 | no | — |
| 189 | C3×D12 | — | 2 | 1 | no | — |
| 190 | C3×D12 | — | 2 | 1 | no | — |
| 191 | C3×C4×D3 | — | 4 | 1 | no | — |
| 192 | C3×C4×D3 | — | 4 | 1 | no | — |
| 193 | C3×Dic6 | — | 2 | 1 | no | — |
| 194 | C3×Dic6 | — | 2 | 1 | no | — |
| 195 | C3⋊(C3⋊C8) | — | 2 | 2 | no | — |
| 196 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 197 | C3×C3⋊C8 | — | 2 | 2 | no | — |
| 198 | C3×C3⋊C8 | — | 4 | 1 | no | — |
| 199 | #575 | — | 3 | 1 | no | — |
| 200 | #575 | — | 9 | 1 | no | — |
| 201 | #575 | — | 9 | 1 | no | — |
| 202 | #408 | — | 3 | 1 | no | — |
| 203 | #408 | — | 9 | 1 | no | — |
| 204 | #408 | — | 9 | 1 | no | — |
| 205 | #338 | — | 9 | 1 | no | — |
| 206 | C3×#41 | — | 2 | 2 | no | — |
| 207 | C3×#41 | — | 2 | 2 | no | — |
| 208 | C3×#41 | — | 2 | 1 | no | — |
| 209 | C3×#41 | — | 2 | 1 | no | — |
| 210 | C3×#41 | — | 2 | 1 | no | — |
| 211 | C3×#41 | — | 2 | 1 | no | — |
| 212 | C3×#41 | — | 2 | 1 | no | — |
| 213 | C3×#41 | — | 2 | 1 | no | — |
| 214 | C3×#41 | — | 2 | 1 | no | — |
| 215 | C3×#41 | — | 2 | 1 | no | — |
| 216 | C3×#41 | — | 4 | 1 | no | — |
| 217 | C3×#41 | — | 4 | 1 | no | — |
| 218 | C3×#41 | — | 6 | 1 | no | — |
| 219 | C3×#41 | — | 6 | 1 | no | — |
| 220 | C3×#41 | — | 6 | 1 | no | — |
| 221 | C3×#41 | — | 6 | 1 | no | — |
| 222 | C2×C3×Q8 | — | 2 | 1 | no | — |
| 223 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 224 | C2×C3×Q8 | D12 | 1 | 1 | yes | characteristic |
| 225 | C2×C3×Q8 | #67 | 1 | 1 | yes | characteristic |
| 226 | C2×C3×D4 | — | 2 | 1 | no | — |
| 227 | C2×C3×D4 | — | 2 | 1 | no | — |
| 228 | C2×C3×D4 | — | 2 | 1 | no | — |
| 229 | C2×C3×D4 | — | 3 | 1 | no | — |
| 230 | C2×C3×D4 | — | 4 | 1 | no | — |
| 231 | C2×C3×D4 | — | 6 | 1 | no | — |
| 232 | C2×C3×D4 | D12 | 1 | 1 | yes | characteristic |
| 233 | C2×C3×D4 | #67 | 1 | 1 | yes | characteristic |
| 234 | C22×C3×C4 | — | 2 | 1 | no | — |
| 235 | C22×C3×C4 | — | 2 | 1 | no | — |
| 236 | C22×C3×C4 | — | 2 | 1 | no | — |
| 237 | C22×C3×C4 | — | 4 | 1 | no | — |
| 238 | C22×C3×C4 | — | 6 | 1 | no | — |
| 239 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 240 | C22×C3×C4 | C22×D3 | 1 | 1 | yes | characteristic |
| 241 | C2×#67 | — | 2 | 1 | no | — |
| 242 | C2×#67 | — | 6 | 1 | no | — |
| 243 | C2×#67 | — | 6 | 1 | no | — |
| 244 | C2×#67 | — | 12 | 1 | no | — |
| 245 | #235 | — | 2 | 1 | no | — |
| 246 | #235 | — | 2 | 1 | no | — |
| 247 | #235 | — | 2 | 1 | no | — |
| 248 | #235 | — | 2 | 1 | no | — |
| 249 | #235 | — | 6 | 2 | no | — |
| 250 | #235 | — | 6 | 2 | no | — |
| 251 | #235 | — | 6 | 1 | no | — |
| 252 | #235 | — | 6 | 1 | no | — |
| 253 | #235 | — | 6 | 1 | no | — |
| 254 | #235 | — | 6 | 1 | no | — |
| 255 | #235 | — | 6 | 1 | no | — |
| 256 | #235 | — | 6 | 1 | no | — |
| 257 | #235 | — | 6 | 1 | no | — |
| 258 | #235 | — | 6 | 1 | no | — |
| 259 | #235 | — | 12 | 1 | no | — |
| 260 | #235 | — | 12 | 1 | no | — |
| 261 | C2×D12 | — | 3 | 1 | no | — |
| 262 | C2×D12 | — | 3 | 1 | no | — |
| 263 | C2×D12 | — | 6 | 1 | no | — |
| 264 | C2×D12 | #67 | 1 | 1 | yes | characteristic |
| 265 | C2×C4×D3 | — | 2 | 1 | no | — |
| 266 | C2×C4×D3 | — | 6 | 1 | no | — |
| 267 | C2×C4×D3 | — | 6 | 1 | no | — |
| 268 | C2×C4×D3 | — | 12 | 1 | no | — |
| 269 | C2×Dic6 | — | 3 | 1 | no | — |
| 270 | C2×Dic6 | — | 3 | 1 | no | — |
| 271 | C2×Dic6 | — | 6 | 1 | no | — |
| 272 | C2×Dic6 | #67 | 1 | 1 | yes | characteristic |
| 273 | C3×Q16 | — | 6 | 2 | no | — |
| 274 | C3×SD16 | — | 6 | 2 | no | — |
| 275 | C3×SD16 | — | 6 | 2 | no | — |
| 276 | C3×D8 | — | 6 | 2 | no | — |
| 277 | C3×M16 | — | 6 | 1 | no | — |
| 278 | C3×M16 | — | 6 | 1 | no | — |
| 279 | C3×M16 | — | 6 | 1 | no | — |
| 280 | C3×M16 | — | 6 | 1 | no | — |
| 281 | C2×C3×C8 | — | 3 | 2 | no | — |
| 282 | C2×C3×C8 | — | 3 | 2 | no | — |
| 283 | C2×C3×C8 | — | 6 | 1 | no | — |
| 284 | C2×C3×C8 | — | 6 | 1 | no | — |
| 285 | C2×C3×C8 | — | 6 | 1 | no | — |
| 286 | #216 | — | 2 | 2 | no | — |
| 287 | #216 | — | 6 | 2 | no | — |
| 288 | #216 | — | 6 | 4 | no | — |
| 289 | #216 | — | 6 | 2 | no | — |
| 290 | #216 | — | 6 | 2 | no | — |
| 291 | #215 | — | 2 | 2 | no | — |
| 292 | #215 | — | 6 | 2 | no | — |
| 293 | #215 | — | 6 | 4 | no | — |
| 294 | #215 | — | 6 | 2 | no | — |
| 295 | #215 | — | 6 | 2 | no | — |
| 296 | #214 | — | 2 | 2 | no | — |
| 297 | #214 | — | 6 | 2 | no | — |
| 298 | #214 | — | 6 | 4 | no | — |
| 299 | #214 | — | 6 | 2 | no | — |
| 300 | #214 | — | 6 | 2 | no | — |
| 301 | #213 | — | 2 | 2 | no | — |
| 302 | #213 | — | 6 | 2 | no | — |
| 303 | #213 | — | 6 | 4 | no | — |
| 304 | #213 | — | 6 | 2 | no | — |
| 305 | #213 | — | 6 | 2 | no | — |
| 306 | #208 | — | 2 | 1 | no | — |
| 307 | #208 | — | 2 | 1 | no | — |
| 308 | #208 | — | 2 | 1 | no | — |
| 309 | #208 | — | 2 | 1 | no | — |
| 310 | #208 | — | 6 | 2 | no | — |
| 311 | #208 | — | 6 | 2 | no | — |
| 312 | #208 | — | 6 | 1 | no | — |
| 313 | #208 | — | 6 | 1 | no | — |
| 314 | #208 | — | 6 | 1 | no | — |
| 315 | #208 | — | 6 | 1 | no | — |
| 316 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 317 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 318 | C2×C3⋊C8 | — | 2 | 1 | no | — |
| 319 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 320 | C2×C3⋊C8 | — | 3 | 2 | no | — |
| 321 | C2×C3⋊C8 | — | 6 | 2 | no | — |
| 322 | C2×C3⋊C8 | #67 | 1 | 2 | yes | — |
| 323 | C2×C3⋊C8 | #67 | 1 | 2 | yes | — |
| 324 | Dic12 | — | 6 | 2 | no | — |
| 325 | D24 | — | 6 | 2 | no | — |
| 326 | #204 | — | 6 | 2 | no | — |
| 327 | #204 | — | 6 | 2 | no | — |
| 328 | C22×C32 | — | 4 | 1 | no | — |
| 329 | C22×C32 | — | 4 | 1 | no | — |
| 330 | C22×C32 | — | 4 | 2 | no | — |
| 331 | C22×C32 | #121 | 1 | 1 | yes | characteristic |
| 332 | C22×C32 | #121 | 1 | 1 | yes | characteristic |
| 333 | C22×C32 | #121 | 1 | 1 | yes | characteristic |
| 334 | C2×C3⋊D3 | — | 4 | 1 | no | — |
| 335 | C2×C3⋊D3 | — | 4 | 2 | no | — |
| 336 | C2×C3×D3 | — | 4 | 2 | no | — |
| 337 | C2×C3×D3 | — | 4 | 1 | no | — |
| 338 | C32×C4 | — | 4 | 1 | no | — |
| 339 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 340 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 341 | C32×C4 | #120 | 1 | 1 | yes | characteristic |
| 342 | C32×C4 | #127 | 1 | 1 | yes | characteristic |
| 343 | C3⋊Dic3 | — | 4 | 1 | no | — |
| 344 | C3×Dic3 | — | 4 | 1 | no | — |
| 345 | C2×#41 | — | 3 | 1 | no | — |
| 346 | C2×#41 | — | 9 | 1 | no | — |
| 347 | C2×#41 | D32 | 1 | 1 | yes | characteristic |
| 348 | #137 | — | 6 | 1 | no | — |
| 349 | #137 | — | 6 | 1 | no | — |
| 350 | #137 | — | 18 | 1 | no | — |
| 351 | #137 | — | 18 | 1 | no | — |
| 352 | #137 | — | 18 | 1 | no | — |
| 353 | #137 | — | 18 | 1 | no | — |
| 354 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 355 | AGL(1,ℤ/8) | — | 6 | 1 | no | — |
| 356 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 357 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 358 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 359 | AGL(1,ℤ/8) | — | 18 | 1 | no | — |
| 360 | #135 | — | 6 | 2 | no | — |
| 361 | #135 | — | 18 | 2 | no | — |
| 362 | #135 | — | 18 | 2 | no | — |
| 363 | C2×M16 | — | 3 | 1 | no | — |
| 364 | C2×M16 | — | 3 | 1 | no | — |
| 365 | C2×M16 | — | 9 | 1 | no | — |
| 366 | C22×C8 | — | 3 | 1 | no | — |
| 367 | C22⋊C8 | — | 6 | 2 | no | — |
| 368 | C22⋊C8 | — | 18 | 2 | no | — |
| 369 | C22⋊C8 | — | 18 | 2 | no | — |
| 370 | C23×C3 | — | 2 | 1 | no | — |
| 371 | C23×C3 | — | 2 | 1 | no | — |
| 372 | C23×C3 | — | 2 | 1 | no | — |
| 373 | C23×C3 | — | 4 | 1 | no | — |
| 374 | C23×C3 | — | 6 | 1 | no | — |
| 375 | C23×C3 | #235 | 1 | 1 | yes | characteristic |
| 376 | C23×C3 | #237 | 1 | 1 | yes | characteristic |
| 377 | C22×D3 | — | 2 | 1 | no | — |
| 378 | C22×D3 | — | 6 | 1 | no | — |
| 379 | C22×D3 | — | 6 | 1 | no | — |
| 380 | C22×D3 | — | 12 | 1 | no | — |
| 381 | C3×Q8 | — | 2 | 2 | no | — |
| 382 | C3×Q8 | — | 2 | 1 | no | — |
| 383 | C3×Q8 | — | 2 | 1 | no | — |
| 384 | C3×Q8 | — | 2 | 1 | no | — |
| 385 | C3×Q8 | — | 2 | 1 | no | — |
| 386 | C3×Q8 | — | 4 | 1 | no | — |
| 387 | C3×Q8 | — | 6 | 1 | no | — |
| 388 | C3×Q8 | — | 6 | 1 | no | — |
| 389 | C3×D4 | — | 2 | 2 | no | — |
| 390 | C3×D4 | — | 2 | 1 | no | — |
| 391 | C3×D4 | — | 2 | 1 | no | — |
| 392 | C3×D4 | — | 2 | 1 | no | — |
| 393 | C3×D4 | — | 2 | 1 | no | — |
| 394 | C3×D4 | — | 4 | 1 | no | — |
| 395 | C3×D4 | — | 4 | 2 | no | — |
| 396 | C3×D4 | — | 4 | 2 | no | — |
| 397 | C3×D4 | — | 4 | 1 | no | — |
| 398 | C3×D4 | — | 4 | 1 | no | — |
| 399 | C3×D4 | — | 4 | 1 | no | — |
| 400 | C3×D4 | — | 4 | 1 | no | — |
| 401 | C3×D4 | — | 6 | 1 | no | — |
| 402 | C3×D4 | — | 6 | 1 | no | — |
| 403 | C3×D4 | — | 12 | 1 | no | — |
| 404 | C3×D4 | — | 12 | 1 | no | — |
| 405 | C2×C3×C4 | — | 2 | 1 | no | — |
| 406 | C2×C3×C4 | — | 2 | 1 | no | — |
| 407 | C2×C3×C4 | — | 2 | 1 | no | — |
| 408 | C2×C3×C4 | — | 2 | 1 | no | — |
| 409 | C2×C3×C4 | — | 2 | 1 | no | — |
| 410 | C2×C3×C4 | — | 2 | 1 | no | — |
| 411 | C2×C3×C4 | — | 2 | 1 | no | — |
| 412 | C2×C3×C4 | — | 2 | 1 | no | — |
| 413 | C2×C3×C4 | — | 4 | 1 | no | — |
| 414 | C2×C3×C4 | — | 4 | 2 | no | — |
| 415 | C2×C3×C4 | — | 4 | 2 | no | — |
| 416 | C2×C3×C4 | — | 4 | 1 | no | — |
| 417 | C2×C3×C4 | — | 4 | 1 | no | — |
| 418 | C2×C3×C4 | — | 4 | 1 | no | — |
| 419 | C2×C3×C4 | — | 4 | 1 | no | — |
| 420 | C2×C3×C4 | — | 6 | 1 | no | — |
| 421 | C2×C3×C4 | — | 12 | 1 | no | — |
| 422 | C2×C3×C4 | — | 12 | 1 | no | — |
| 423 | C2×C3×C4 | C2×D12 | 1 | 1 | yes | characteristic |
| 424 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 425 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 426 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 427 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 428 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 429 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 430 | C2×C3×C4 | D3×D4 | 1 | 1 | yes | characteristic |
| 431 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 432 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 433 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 434 | C2×C3×C4 | C2×#67 | 1 | 1 | yes | characteristic |
| 435 | #67 | — | 4 | 1 | no | — |
| 436 | #67 | — | 4 | 1 | no | — |
| 437 | #67 | — | 12 | 2 | no | — |
| 438 | #67 | — | 12 | 2 | no | — |
| 439 | #67 | — | 12 | 1 | no | — |
| 440 | #67 | — | 12 | 1 | no | — |
| 441 | #67 | — | 12 | 1 | no | — |
| 442 | #67 | — | 12 | 1 | no | — |
| 443 | C2×Dic3 | — | 2 | 1 | no | — |
| 444 | C2×Dic3 | — | 6 | 1 | no | — |
| 445 | C2×Dic3 | — | 6 | 1 | no | — |
| 446 | C2×Dic3 | — | 12 | 1 | no | — |
| 447 | D12 | — | 2 | 1 | no | — |
| 448 | D12 | — | 2 | 1 | no | — |
| 449 | D12 | — | 6 | 2 | no | — |
| 450 | D12 | — | 6 | 1 | no | — |
| 451 | D12 | — | 6 | 1 | no | — |
| 452 | D12 | — | 6 | 1 | no | — |
| 453 | D12 | — | 6 | 1 | no | — |
| 454 | D12 | — | 12 | 1 | no | — |
| 455 | C4×D3 | — | 4 | 1 | no | — |
| 456 | C4×D3 | — | 4 | 1 | no | — |
| 457 | C4×D3 | — | 12 | 2 | no | — |
| 458 | C4×D3 | — | 12 | 2 | no | — |
| 459 | C4×D3 | — | 12 | 1 | no | — |
| 460 | C4×D3 | — | 12 | 1 | no | — |
| 461 | C4×D3 | — | 12 | 1 | no | — |
| 462 | C4×D3 | — | 12 | 1 | no | — |
| 463 | Dic6 | — | 2 | 1 | no | — |
| 464 | Dic6 | — | 2 | 1 | no | — |
| 465 | Dic6 | — | 6 | 2 | no | — |
| 466 | Dic6 | — | 6 | 1 | no | — |
| 467 | Dic6 | — | 6 | 1 | no | — |
| 468 | Dic6 | — | 6 | 1 | no | — |
| 469 | Dic6 | — | 6 | 1 | no | — |
| 470 | Dic6 | — | 12 | 1 | no | — |
| 471 | C3×C8 | — | 6 | 2 | no | — |
| 472 | C3×C8 | — | 6 | 2 | no | — |
| 473 | C3×C8 | — | 12 | 1 | no | — |
| 474 | C3⋊C8 | — | 2 | 2 | no | — |
| 475 | C3⋊C8 | — | 2 | 2 | no | — |
| 476 | C3⋊C8 | — | 4 | 1 | no | — |
| 477 | C3⋊C8 | — | 6 | 4 | no | — |
| 478 | C3⋊C8 | — | 6 | 2 | no | — |
| 479 | C3⋊C8 | — | 6 | 2 | no | — |
| 480 | C2×C32 | — | 2 | 1 | no | — |
| 481 | C2×C32 | — | 2 | 1 | no | — |
| 482 | C2×C32 | — | 2 | 1 | no | — |
| 483 | C2×C32 | — | 8 | 1 | no | — |
| 484 | C2×C32 | #392 | 1 | 1 | yes | characteristic |
| 485 | C3⋊D3 | — | 8 | 1 | no | — |
| 486 | C3×D3 | — | 8 | 1 | no | — |
| 487 | #41 | — | 2 | 1 | no | — |
| 488 | #41 | — | 2 | 1 | no | — |
| 489 | #41 | — | 2 | 1 | no | — |
| 490 | #41 | — | 2 | 1 | no | — |
| 491 | #41 | — | 6 | 1 | no | — |
| 492 | #41 | — | 6 | 1 | no | — |
| 493 | #41 | — | 6 | 1 | no | — |
| 494 | #41 | — | 6 | 1 | no | — |
| 495 | #41 | — | 18 | 1 | no | — |
| 496 | #41 | — | 18 | 1 | no | — |
| 497 | #41 | — | 18 | 1 | no | — |
| 498 | #41 | — | 18 | 1 | no | — |
| 499 | C2×Q8 | — | 3 | 1 | no | — |
| 500 | C2×Q8 | — | 9 | 1 | no | — |
| 501 | C2×Q8 | #626 | 1 | 1 | yes | characteristic |
| 502 | C2×D4 | — | 2 | 1 | no | — |
| 503 | C2×D4 | — | 3 | 1 | no | — |
| 504 | C2×D4 | — | 6 | 1 | no | — |
| 505 | C2×D4 | — | 9 | 1 | no | — |
| 506 | C2×D4 | — | 18 | 1 | no | — |
| 507 | C2×D4 | #626 | 1 | 1 | yes | characteristic |
| 508 | C22×C4 | — | 2 | 1 | no | — |
| 509 | C22×C4 | — | 6 | 1 | no | — |
| 510 | C22×C4 | — | 18 | 1 | no | — |
| 511 | C22×C4 | C2×D32 | 1 | 1 | yes | characteristic |
| 512 | Q16 | — | 6 | 2 | no | — |
| 513 | Q16 | — | 18 | 2 | no | — |
| 514 | Q16 | — | 18 | 2 | no | — |
| 515 | SD16 | — | 6 | 2 | no | — |
| 516 | SD16 | — | 6 | 2 | no | — |
| 517 | SD16 | — | 18 | 2 | no | — |
| 518 | SD16 | — | 18 | 2 | no | — |
| 519 | SD16 | — | 18 | 2 | no | — |
| 520 | SD16 | — | 18 | 2 | no | — |
| 521 | D8 | — | 6 | 2 | no | — |
| 522 | D8 | — | 18 | 2 | no | — |
| 523 | D8 | — | 18 | 2 | no | — |
| 524 | M16 | — | 6 | 1 | no | — |
| 525 | M16 | — | 6 | 1 | no | — |
| 526 | M16 | — | 6 | 1 | no | — |
| 527 | M16 | — | 6 | 1 | no | — |
| 528 | M16 | — | 18 | 1 | no | — |
| 529 | M16 | — | 18 | 1 | no | — |
| 530 | C2×C8 | — | 3 | 2 | no | — |
| 531 | C2×C8 | — | 3 | 2 | no | — |
| 532 | C2×C8 | — | 6 | 1 | no | — |
| 533 | C2×C8 | — | 6 | 1 | no | — |
| 534 | C2×C8 | — | 6 | 1 | no | — |
| 535 | C2×C8 | — | 9 | 2 | no | — |
| 536 | C22×C3 | — | 2 | 1 | no | — |
| 537 | C22×C3 | — | 2 | 1 | no | — |
| 538 | C22×C3 | — | 2 | 1 | no | — |
| 539 | C22×C3 | — | 4 | 1 | no | — |
| 540 | C22×C3 | — | 4 | 1 | no | — |
| 541 | C22×C3 | — | 4 | 2 | no | — |
| 542 | C22×C3 | — | 4 | 2 | no | — |
| 543 | C22×C3 | — | 4 | 2 | no | — |
| 544 | C22×C3 | — | 4 | 1 | no | — |
| 545 | C22×C3 | — | 4 | 1 | no | — |
| 546 | C22×C3 | — | 8 | 1 | no | — |
| 547 | C22×C3 | — | 8 | 2 | no | — |
| 548 | C22×C3 | — | 12 | 2 | no | — |
| 549 | C22×C3 | — | 12 | 1 | no | — |
| 550 | C22×C3 | #884 | 1 | 1 | yes | characteristic |
| 551 | C22×C3 | #884 | 1 | 1 | yes | characteristic |
| 552 | C22×C3 | #930 | 1 | 1 | yes | characteristic |
| 553 | C22×C3 | #938 | 1 | 1 | yes | characteristic |
| 554 | C22×C3 | #939 | 1 | 1 | yes | characteristic |
| 555 | C22×C3 | #939 | 1 | 1 | yes | characteristic |
| 556 | C2×D3 | — | 4 | 2 | no | — |
| 557 | C2×D3 | — | 4 | 1 | no | — |
| 558 | C2×D3 | — | 12 | 2 | no | — |
| 559 | C2×D3 | — | 12 | 2 | no | — |
| 560 | C2×D3 | — | 12 | 2 | no | — |
| 561 | C2×D3 | — | 12 | 1 | no | — |
| 562 | C2×D3 | — | 12 | 1 | no | — |
| 563 | C2×D3 | — | 24 | 2 | no | — |
| 564 | C3×C4 | — | 2 | 1 | no | — |
| 565 | C3×C4 | — | 2 | 1 | no | — |
| 566 | C3×C4 | — | 2 | 1 | no | — |
| 567 | C3×C4 | — | 2 | 1 | no | — |
| 568 | C3×C4 | — | 4 | 2 | no | — |
| 569 | C3×C4 | — | 4 | 1 | no | — |
| 570 | C3×C4 | — | 4 | 1 | no | — |
| 571 | C3×C4 | — | 12 | 1 | no | — |
| 572 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 573 | C3×C4 | #882 | 1 | 1 | yes | characteristic |
| 574 | C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 575 | C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 576 | C3×C4 | #937 | 1 | 1 | yes | characteristic |
| 577 | C3×C4 | #940 | 1 | 1 | yes | characteristic |
| 578 | C3×C4 | #940 | 1 | 1 | yes | characteristic |
| 579 | C3×C4 | #953 | 1 | 1 | yes | characteristic |
| 580 | Dic3 | — | 4 | 1 | no | — |
| 581 | Dic3 | — | 12 | 2 | no | — |
| 582 | Dic3 | — | 12 | 1 | no | — |
| 583 | Dic3 | — | 12 | 1 | no | — |
| 584 | C32 | #2017 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 585 | C23 | — | 2 | 1 | no | — |
| 586 | C23 | — | 6 | 1 | no | — |
| 587 | C23 | — | 18 | 1 | no | — |
| 588 | C23 | #3804 | 1 | 1 | yes | characteristic |
| 589 | Q8 | — | 2 | 1 | no | — |
| 590 | Q8 | — | 2 | 1 | no | — |
| 591 | Q8 | — | 6 | 1 | no | — |
| 592 | Q8 | — | 6 | 1 | no | — |
| 593 | Q8 | — | 18 | 1 | no | — |
| 594 | Q8 | — | 18 | 1 | no | — |
| 595 | D4 | — | 2 | 1 | no | — |
| 596 | D4 | — | 2 | 1 | no | — |
| 597 | D4 | — | 4 | 1 | no | — |
| 598 | D4 | — | 4 | 1 | no | — |
| 599 | D4 | — | 6 | 1 | no | — |
| 600 | D4 | — | 6 | 1 | no | — |
| 601 | D4 | — | 12 | 1 | no | — |
| 602 | D4 | — | 12 | 1 | no | — |
| 603 | D4 | — | 18 | 1 | no | — |
| 604 | D4 | — | 18 | 1 | no | — |
| 605 | D4 | — | 36 | 1 | no | — |
| 606 | D4 | — | 36 | 1 | no | — |
| 607 | C2×C4 | — | 2 | 1 | no | — |
| 608 | C2×C4 | — | 4 | 1 | no | — |
| 609 | C2×C4 | — | 4 | 1 | no | — |
| 610 | C2×C4 | — | 6 | 1 | no | — |
| 611 | C2×C4 | — | 12 | 1 | no | — |
| 612 | C2×C4 | — | 12 | 1 | no | — |
| 613 | C2×C4 | — | 18 | 1 | no | — |
| 614 | C2×C4 | — | 36 | 1 | no | — |
| 615 | C2×C4 | — | 36 | 1 | no | — |
| 616 | C2×C4 | C2×#626 | 1 | 1 | yes | characteristic |
| 617 | C2×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 618 | C2×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 619 | C2×C4 | D3×#67 | 1 | 1 | yes | characteristic |
| 620 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 621 | C2×C4 | #3811 | 1 | 1 | yes | characteristic |
| 622 | C8 | — | 6 | 2 | no | — |
| 623 | C8 | — | 6 | 2 | no | — |
| 624 | C8 | — | 12 | 1 | no | — |
| 625 | C8 | — | 18 | 2 | no | — |
| 626 | C2×C3 | — | 2 | 1 | no | — |
| 627 | C2×C3 | — | 2 | 1 | no | — |
| 628 | C2×C3 | — | 2 | 1 | no | — |
| 629 | C2×C3 | — | 2 | 1 | no | — |
| 630 | C2×C3 | — | 2 | 1 | no | — |
| 631 | C2×C3 | — | 2 | 1 | no | — |
| 632 | C2×C3 | — | 2 | 1 | no | — |
| 633 | C2×C3 | — | 4 | 1 | no | — |
| 634 | C2×C3 | — | 4 | 1 | no | — |
| 635 | C2×C3 | — | 4 | 1 | no | — |
| 636 | C2×C3 | — | 8 | 2 | no | — |
| 637 | C2×C3 | — | 8 | 1 | no | — |
| 638 | C2×C3 | — | 8 | 1 | no | — |
| 639 | C2×C3 | — | 24 | 1 | no | — |
| 640 | C2×C3 | #4960 | 1 | 1 | yes | characteristic |
| 641 | C2×C3 | #5223 | 1 | 1 | yes | characteristic |
| 642 | D3 | — | 8 | 1 | no | — |
| 643 | D3 | — | 24 | 2 | no | — |
| 644 | D3 | — | 24 | 1 | no | — |
| 645 | D3 | — | 24 | 1 | no | — |
| 646 | C22 | — | 4 | 1 | no | — |
| 647 | C22 | — | 4 | 2 | no | — |
| 648 | C22 | — | 4 | 1 | no | — |
| 649 | C22 | — | 12 | 2 | no | — |
| 650 | C22 | — | 12 | 1 | no | — |
| 651 | C22 | — | 36 | 2 | no | — |
| 652 | C22 | — | 36 | 1 | no | — |
| 653 | C22 | #63958 | 1 | 1 | yes | characteristic |
| 654 | C22 | #63971 | 1 | 1 | yes | characteristic |
| 655 | C22 | #63978 | 1 | 1 | yes | characteristic |
| 656 | C4 | — | 4 | 1 | no | — |
| 657 | C4 | — | 12 | 1 | no | — |
| 658 | C4 | — | 36 | 1 | no | — |
| 659 | C4 | #63977 | 1 | 1 | yes | characteristic |
| 660 | C4 | #63979 | 1 | 1 | yes | characteristic |
| 661 | C4 | #63981 | 1 | 1 | yes | characteristic |
| 662 | C4 | #63983 | 1 | 1 | yes | characteristic |
| 663 | C3 | — | 2 | 1 | no | — |
| 664 | C3 | #70013 | 1 | 1 | yes | characteristic, complemented |
| 665 | C3 | #72121 | 1 | 1 | yes | characteristic, complemented |
| 666 | C2 | — | 2 | 1 | no | — |
| 667 | C2 | — | 2 | 1 | no | — |
| 668 | C2 | — | 2 | 1 | no | — |
| 669 | C2 | — | 8 | 1 | no | — |
| 670 | C2 | — | 24 | 1 | no | — |
| 671 | C2 | — | 72 | 1 | no | — |
| 672 | C2 | #10591724 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10596293 | C2 | semidirect |
| 2. C3×#5822 | C2 | semidirect |
| 3. #10594795 | C2 | semidirect |
| 4. C3×#5234 | C2 | semidirect |
| 5. #10591073 | C2 | semidirect |
| 6. #10591070 | C2 | semidirect |
| 7. #10589159 | C2 | semidirect |
| 40. #5822 | D3 | semidirect |
| 44. #5234 | D3 | semidirect |
| 584. C32 | #2017 | semidirect |
| 664. C3 | #70013 | semidirect |
| 665. C3 | #72121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596293 | 2 |
| C3×#5822 | 2 |
| #10594795 | 2 |
| C3×#5234 | 2 |
| #10591073 | 2 |
| #10591070 | 2 |
| #10589159 | 2 |
| #72121 | 3 |
| #70013 | 3 |